Book/Report

FZJ-2017-04427

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png On the treatment of an elliptic boundary value problem in plasma physics with the aid of FORMAC

Belitz, H. J. (Corresponding author)FZJ*

1970
Kernforschungsanlage Jülich, Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/14814

Report No.: Juel-0663-PP

Abstract: The elliptic differential equation $\bigg(\frac{\partial^{2}}{\partial \gamma^{2}} - \frac{1}{\gamma} \frac{\partial}{\partial \gamma} + \frac{\partial^{2}}{\partial \gamma^{2}}\bigg) \Psi (x, z) = f_{o}(x, z) + f_{1}(x, z; \Psi)$, where x = r - R$_{o}$ and f$_{1}$ is a polynom in $\Psi$ up to $\Psi^{4}$ has been treated with the boundary condition $\Psi$ = 0 on a surface $\sum$, defined by $\sum : x^{2} + z^{2} - p^{2} = 0$ Assuming $\Psi = (x^{2} + z^{2} -p^{2}) \sum^{i_{max}}_{i=0} \sum^{j_{max}}_{j=0} C_{ij}x^{i}z^{2j}$ the coefficients $C_{ij}$ have been calculated up to $i_{max} + j_{max} = 10.$ The method is applicable to higher orders in x and z; a general recurrent formula for the coefficients, has not yet been found. The convergence problem is still open and will be treated in a later paper. Two numerical examples of a parameter study are given.

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Contributing Institute(s):

1. Publikationen vor 2000 (PRE-2000)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

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